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This paper is concerned with a class of linear–quadratic stochastic large-population problems with partial information, where the individual agent only has access to a noisy observation process related to the state. The dynamics of each agent follows a linear stochastic differential equation driven by the individual noise, and all agents are coupled together via the control average term. By studying the associated mean-field game and using the backward separation principle with a state decomposition technique, the decentralized optimal control can be obtained in the open-loop form through a forward–backward stochastic differential equation with the conditional expectation. The optimal filtering equation is also provided. Thanks to the decoupling method, the decentralized optimal control can also be further presented as the feedback of state filtering via the Riccati equation. The explicit solution of the control average limit is given, and the consistency condition system is discussed. Moreover, the related $\varepsilon$-Nash equilibrium property is verified. To illustrate the good performance of theoretical results, an example in finance is studied.

Motivated by the linearized model of unstable burning in solid propellant rockets, this article addresses the adaptive event-triggered output feedback control of uncertain parabolic PDEs. First, we construct an adaptive identifier that consists of a gradient estimator, and then design a continuous-in-time controller. On this basis, we design a novel event-triggered output feedback controller and construct dynamic triggering conditions to assure the global asymptotic stability of the closed-loop system around the limit points. Furthermore, the parameter estimation is proven to converge to the true value when an additional constant input at the boundary is applied to the closed-loop system. Finally, simulation data verifies the effectiveness of the theoretical analysis.

This paper is concerned with security controller design of unknown networked systems under aperiodic denial-of-service (DoS) attacks, using only noise data but no model knowledge. First, a novel attack parameter-dependent stability criterion of linear networked systems under a class of time-constraint DoS attacks is proposed by using DoS attack parameter-dependent time-varying Lyapunov function method, where the considered system model, the state-feedback gain, and the lower and upper bounds of sleeping/active periods of DoS attack signal are known in advance. Based on this model-based stability condition and by combining tools from data-driven control theory, robust control theory, and switched system approach to security control, a new data-based stability criterion of all linear networked control systems (NCSs) which are consistent with the measured data and the assumed noise bound in the presence of DoS attacks is derived in terms of linear matrix inequalities. Based on this data-dependent parametrization, the data-driven security state-feedback controllers are designed correspondingly. Our control method guarantees the exponential stability properties robustly for all linear systems consistent with the measured data despite the presence of DoS attacks. As a byproduct, the proposed method embeds existing approaches for event-triggered control (ETC) into a general data-based event-triggered security control framework, which can be extended to co-design of data-based robust controller and event-triggering mechanism for uncertain NCSs under DoS attacks. Finally, the efficiency and superiority of the proposed methodology are verified through a numerical example.

This paper presents weighted stochastic Riccati (WSR) equations for designing multiple types of controllers for linear stochastic systems. The system matrices are independent and identically distributed (i.i.d.) to represent noise in the systems. While the stochasticity can invoke unpredictable control results, it is essentially difficult to design controllers for systems with i.i.d. matrices because the controllers can be solutions to non-algebraic equations. Although an existing method has tackled this difficulty, the method has not realized the generality because it relies on the special form of cost functions for risk-sensitive linear (RSL) control. Furthermore, designing controllers over an infinite-horizon remains challenging because many iterations of solving nonlinear optimization is needed. To overcome these problems, the proposed WSR equations employ a weighted expectation of stochastic equations. Solutions to the WSR equations provide multiple types of controllers characterized by the weight, which contain stochastic optimal and RSL controllers. Two approaches calculating simple recursive formulas are proposed to solve the WSR equations without solving the nonlinear optimization. Moreover, designing the weight yields a novel controller termed the robust RSL controller that has both a risk-sensitive policy and robustness to randomness occurring in stochastic controller design.

We study a multi-agent resilient consensus problem, where some agents are of the Byzantine type and try to prevent the normal ones from reaching consensus. In our setting, normal agents communicate with each other asynchronously over multi-hop relay channels with delays. To solve this asynchronous Byzantine consensus problem, we develop the multi-hop weighted mean subsequence reduced (MW-MSR) algorithm. The main contribution is that we characterize a tight graph condition for our algorithm to achieve Byzantine consensus, which is expressed in the novel notion of strictly robust graphs. We show that the multi-hop communication is effective for enhancing the network’s resilience against Byzantine agents. As a result, we also obtain novel conditions for resilient consensus under the malicious attack model, which are tighter than those known in the literature. Furthermore, the proposed algorithm can be viewed as a generalization of the conventional flooding-based algorithms, with less computational complexity. Lastly, we provide numerical examples to show the effectiveness of the proposed algorithm.

The famous discretized Lyapunov functional method of K. Gu employing the functionals of general structure with piecewise linear matrix kernels is known to deliver effective stability conditions in the form of linear matrix inequalities (LMIs). In parallel, the role of the delay Lyapunov matrix for linear time-invariant systems with delay was recently revealed. In Gomez et al. (2019), it was shown that the positive definiteness of a beautiful block matrix which involves the delay Lyapunov matrix values at several discretization points of the delay interval constitutes a necessary and sufficient condition for the exponential stability. The only drawback is that the dimension of the block matrix turns out to be very high in practice. In this study, we significantly reduce the dimension by combining the delay Lyapunov matrix framework with the discretized Lyapunov functional method. The component of the latter method that pertains to the discretization of the functional derivative is replaced with bounding the difference between the values of the functional possessing a prescribed derivative and its discretized counterpart. The key breakthrough lies in the fact that the structure of the block matrix is kept the same as in Gomez et al. (2019). Numerical examples show the superiority of our method in many cases compared to the other techniques known in the literature.

This note is concerned with the stability analysis problem of stochastic neutral-type time-delay systems with multiple delays. A less restrictive constraint is imposed to ensure that the difference operator (which appears on the left hand side of the stochastic neutral-type time-delay systems) possesses the property that “exponentially converging input implies exponentially converging state”. Such a constraint is necessary and sufficient for the strong stability of the difference equation associated with the system in the deterministic setting, and thus cannot be further relaxed.

In this paper, we introduce a set representation called polynomial logical zonotopes for performing exact and computationally efficient reachability analysis on logical systems. We prove that through this polynomial-like construction, we are able to perform all of the fundamental logical operations (XOR, NOT, XNOR, AND, NAND, OR, NOR) between sets of points exactly in a reduced space, i.e., generator space with reduced complexity. Polynomial logical zonotopes are a generalization of logical zonotopes, which are able to represent up to $2^{\gamma }$ binary vectors using only $\gamma$ generators. Due to their construction, logical zonotopes are only able to support exact computations of some logical operations (XOR, NOT, XNOR), while other operations (AND, NAND, OR, NOR) result in over-approximations in the generator space. In order to perform all fundamental logical operations exactly, we formulate a generalization of logical zonotopes that is constructed by dependent generators and exponent matrices. While we are able to perform all of the logical operations exactly, this comes with a slight increase in computational complexity compared to logical zonotopes. To illustrate and showcase the computational benefits of polynomial logical zonotopes, we present the results of performing reachability analysis on two use cases: (1) safety verification of an intersection crossing protocol and (2) reachability analysis on a high-dimensional Boolean function. Moreover, to highlight the extensibility of logical zonotopes, we include an additional use case where we perform a computationally tractable exhaustive search for the key of a linear feedback shift register.

The paper focuses on the set-estimation for uncertain Max-Plus Linear systems, with bounded random parameters. This estimation process involves determining the conditional reach set, which is a compact set of all possible states that can be reached from a previous set through the transition model (dynamics) and can lead to the observed measurements through the observation model. In the context of Bayesian estimation theory, this set represents the support of the posterior probability density function of the system’s state. We compare two approaches, a disjunctive approach, presented in literature, and a concise approach, presented as a contribution of this paper, to exactly compute this set. Even if both approaches are with an exponential theoretical complexity, it is shown that the concise approach is more efficient.

This paper focuses on the boundary stabilization control of a rotating disk–beam–mass system (DBMS), comprised of a one-dimensional flexible beam perpendicularly affixed to a rotating rigid disk at its lower boundary and a payload, conceptualized as a tip mass at its opposite end. We posit that the boundary control, which includes an external torque acting on the disk and an external force acting on the tip mass, is subject to an undefined time-varying disturbance. Concurrently, the flexible beam experiences an undefined spatiotemporal-varying distributed disturbance. Firstly, we employ Hamilton’s principle to elaborate on the mathematical model that describes the motion of DBMS. Subsequently, an adaptive boundary control is designed to stabilize the beam’s transverse displacement and regulate the disk’s angular velocity to track a predetermined value asymptotically. Applying the theory of Lyapunov, we demonstrate that uniform and ultimate boundedness under distributed disturbance can be achieved. Finally, we conduct several numerical simulations to showcase the applicability and efficacy of our proposed adaptive boundary controller.